Question

The height of a photograph is 40 cm greater than the width, and the area of the photograph is 896 cm2what is the height of the photograph?

Answer 1

Height = 56 cm

Explanation:

let the width of photograph be = 'w' cm

let the Height of photograph be = 'h' cm

Now it is given that height is 40 cm greater than width

=> h = w + 40 cm.............................(i)

Now it is given that area of photograph =
`896cm^(2)`

We know that area =
`Width^{}`x
`Height^{}`

Thus we have
`h^{}` x
`w^{}`=
`896cm^(2)`

Applying value of 'h' from equation i we get

`(w+40^{})`x
`w^{}`=
`896cm^(2)`

`w^(2) +40w=896cm^(2)`

This is a quadratic equation in 'w' whose solution in standard form is given by

w=
`\frac{-b\mp\sqrt{b^(2)-4ac}}{2a}`

upon comparing with standard equation we see that

a =1

b=40

c=896

applying values in the formula we get

w=
`\frac{-40\mp\sqrt{40^(2)-4* 1*- 896}}{2 *1 }`

w1 = 16 cm

w2 = -56 cm

We discard -56 cm since length cannot be negative thus

width = 16 cm

Height = 40+16 cm = 56 cm